A statistical-physics-based model may shed light on the age-old question "how can morality take root in a world where everyone is out for themselves?" Computer simulations by an international team of scientists suggest that the answer lies in how people interact with their closest neighbours rather than with the population as a whole.

Led by Dirk Helbing of ETH Zurich in Switzerland, the study also suggests that under certain conditions, dishonest behaviour of some individuals can actually improve the social fabric.

Public goods such as environmental resources or social benefits are often depleted because self-interested individuals ignore the common good. Co-operative behaviour can be enforced via punishment but ultimately co-operators who punish will lose out to co-operators who don't punish because punishing requires time and effort. These non-punishing co-operators then lose out to the non co-operators, or free riders. With free riders dominant the resource is depleted, to the detriment of everyone – a scenario known as "tragedy of the commons".

How, then, does co-operation arise? Some researchers have proposed that co-operators who punish could survive through "indirect reciprocity", the idea that working for the common good will enhance a person's reputation and ensure that they benefit in the future. Helbing's group, however, has shown that this is not needed for co-operation to flourish.

Emergent phenomena

They came to this conclusion by focusing on how individuals behave with their nearest neighbours, rather than a wider group that is representative of the entire population. Like nearest-neighbour models of magnetism – which are often more realistic than mean-field approximations – they say that this approach captures "emergent" phenomena that would otherwise be lost.

Their game-theory-based model comprises a square lattice of tens of thousands of points, each representing an individual. Each individual could adopt one of four strategies – co-operate without punishing free riders; co-operate and punish ("moralist"); free ride; or free ride but also punish other free riders ("immoralist"). Initially, the four strategies are distributed randomly among individuals and the system evolves to find out which behaviour wins in the long run.

This evolution is influenced by three variables – the fines that penalize free riders; the cost of administering punishment; and the "synergy factor", which stipulates how much the sum of individual contributions is enhanced by collective action.

The computer program picks an individual at random and calculates how much it stands to gain relative to its four nearest neighbours, given the strategies employed by each neighbour. The exercise is then repeated for the neighbours themselves. The strategy employed by each individual was then modified in light of the success of their neighbours, so that individuals could imitate those who performed better than themselves.

Intriguing results

Running the simulation for up to 10 million iterations yielded some intriguing results. As expected, if the punishment fine to cost ratio and synergy factor were low then everyone would eventually become a free rider, just as moralists would prevail if the fine was set high enough. However, they also found that moralists could win out over non-punishing co-operators even if the cost of administering punishment was relatively high. This was because imitation of better-performing neighbours soon led to small clusters of both co-operators and moralists in a sea of free-riders. With moralists better than co-operators at dealing with free riders they came to dominate, even though they would lose out if placed in direct competition with the non-punishers.

An "unholy collaboration" between moralists and immoralists was also seen whereby individuals adopting these strategies could coexist at the expense of both co-operators and free riders. This, the researchers found, would occur if the cost of punishment was low, the synergy not particularly high, and the fines moderately high. As they point out, this scenario is supported by the real-life existence of immoralists.

New type of collective behaviour

Helbing's colleague, Attila Szolnoki of the Institute for Technical Physics and Materials Science in Budapest sums up the work, "The contribution of statistical physics to this research field could be to realize that large numbers of players can result in a new type of collective behaviour that cannot be derived from two-player analyses. Computer models can therefore be considered as pre-experiments that help to design more sophisticated lab experiments."

The team is currently building a laboratory capable of carrying out game-theory experiments with up to 36 people, which should allow them to test the predictions of their model.

Herbert Gintis, an economist and game-theory expert at the Santa Fe Institute and Central European University in Budapest, believes that Helbing and colleagues are right to incorporate small-scale interactions into their model. But he says that they should also factor in genetic relations between people because individuals' behaviours depend on whether or not they are dealing with a close relative.